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vampirchik [111]

2 years ago

9

The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each

shaded part. Give your answer as a completely simplified exact value in terms of π (no approximations).

1 answer:

Colt1911 [192]2 years ago

7 0

The answer is 2.5 because you need to divide it and then you get your answer

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Let f = ay i + bz j + cx k where a, b, and c are positive constants. let c be the triangle obtained by tracing out the path from

oee [108]

You can either compute three line integrals, or use Stokes' theorem and compute one surface integral. I prefer the latter.

The curl of the given vector field is

$\nabla\times\mathbf f(x,y,z)=-b\,\mathbf i-c\,\mathbf j-a\,\mathbf k$

Parameterize the triangular surface bounded by $\mathcal C$ - I'll call it $\mathcal S$ - by

$\mathbf s(u,v)=7\,\mathbf i+6v\,\mathbf j+2(u+v-uv)\,\mathbf k$

with $0\le u\le1$ and $0\le v\le1$ . By Stokes' theorem, we have

$\displaystyle\int_{\mathcal C}\mathbf f(x,y,z)\cdot\mathrm d\mathbf r=\iint_{\mathcal S}\nabla\times\mathbf f(x,y,z)\cdot\mathrm d\mathbf S$

where $\mathcal S$ is positively oriented; that is, every vector normal to $\mathcal S$ is pointed in the positive $x$ direction. The surface element is given by

$\mathrm d\mathbf S=\mathbf s_u\times\mathbf s_v\,\mathrm du\,\mathrm dv$

So our integral is

$\displaystyle\int_{v=0}^{v=1}\int_{u=0}^{u=1}(-b\,\mathbf i-c\,\mathbf j-a\,\mathbf k)\cdot((12v-12)\,\mathbf i)\,\mathrm du\,\mathrm dv$
$\displaystyle=12b\int_{v=0}^{v=1}(1-v)\,\mathrm dv=6b$

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3 years ago

Slope-intercept form of the line that goes through the points (-9, 10) and (-7, 2)

Lady_Fox [76]

The answer is Y=-4x-26

7 0

3 years ago

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greta collects the number of miles run each week from random sample of female marathon runners. her data are shown below. she ma

dedylja [7]

Her statement is not reasonable because it is not true that 25% of female marathoners run 13 or more miles a week, it is true that 25% run less than 13 miles a week (out of the data). The rest of the data would be 75%, making the statement, "75% of female marathoners run 13 or more miles a week" true. The way she recorded the data does not interfere with the statement being reasonable since it is unbiased.

8 0

3 years ago

A catfish pond contains 2,200 gallons of water. The pond can hold no more than 3,000 gallons. It is being filled at a rate of 12

Olenka [21]

Answer:

I am not sure honestly, but I think you should

Step-by-step explanation:

add 2,200 and 3,000 then see your answer, and divide it by 125. I'm sorry if this doesn't help......

8 0

3 years ago

What 1,055 to the nearest tenth

Burka [1]

1,060 hope this helped !

7 0

3 years ago

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